| The Compound Interest Calculator below can be used to compare or convert the interest rates of different compounding periods. Please use our Interest Calculator to do actual calculations on compound interest. Related Interest Calculator | Investment Calculator | Auto Loan CalculatorInterest is the cost of using borrowed money, or more specifically, the amount a lender receives for advancing money to a borrower. When paying interest, the borrower will mostly pay a percentage of the principal (the borrowed amount). The concept of interest can be categorized into simple interest or compound interest. Simple interest refers to interest earned only on the principal, usually denoted as a specified percentage of the principal. To determine an interest payment, simply multiply principal by the interest rate and the number of periods for which the loan remains active. For example, if one person borrowed $100 from a bank at a simple interest rate of 10% per year for two years, at the end of the two years, the interest would come out to: $100 × 10% × 2 years = $20 Simple interest is rarely used in the real world. Compound interest is widely used instead. Compound interest is interest earned on both the principal and on the accumulated interest. For example, if one person borrowed $100 from a bank at a compound interest rate of 10% per year for two years, at the end of the first year, the interest would amount to: $100 × 10% × 1 year = $10 At the end of the first year, the loan's balance is principal plus interest, or $100 + $10, which equals $110. The compound interest of the second year is calculated based on the balance of $110 instead of the principal of $100. Thus, the interest of the second year would come out to: $110 × 10% × 1 year = $11 The total compound interest after 2 years is $10 + $11 = $21 versus $20 for the simple interest. Because lenders earn interest on interest, earnings compound over time like an exponentially growing snowball. Therefore, compound interest can financially reward lenders generously over time. The longer the interest compounds for any investment, the greater the growth. As a simple example, a young man at age 20 invested $1,000 into the stock market at a 10% annual return rate, the S&P 500's average rate of return since the 1920s. At the age of 65, when he retires, the fund will grow to $72,890, or approximately 73 times the initial investment! While compound interest grows wealth effectively, it can also work against debtholders. This is why one can also describe compound interest as a double-edged sword. Putting off or prolonging outstanding debt can dramatically increase the total interest owed. Different compounding frequenciesInterest can compound on any given frequency schedule but will typically compound annually or monthly. Compounding frequencies impact the interest owed on a loan. For example, a loan with a 10% interest rate compounding semi-annually has an interest rate of 10% / 2, or 5% every half a year. For every $100 borrowed, the interest of the first half of the year comes out to: $100 × 5% = $5 For the second half of the year, the interest rises to: ($100 + $5) × 5% = $5.25 The total interest is $5 + $5.25 = $10.25. Therefore, a 10% interest rate compounding semi-annually is equivalent to a 10.25% interest rate compounding annually. The interest rates of savings accounts and Certificate of Deposits (CD) tend to compound annually. Mortgage loans, home equity loans, and credit card accounts usually compound monthly. Also, an interest rate compounded more frequently tends to appear lower. For this reason, lenders often like to present interest rates compounded monthly instead of annually. For example, a 6% mortgage interest rate amounts to a monthly 0.5% interest rate. However, after compounding monthly, interest totals 6.17% compounded annually. Our compound interest calculator above accommodates the conversion between daily, bi-weekly, semi-monthly, monthly, quarterly, semi-annual, annual, and continuous (meaning an infinite number of periods) compounding frequencies. Compound interest formulasThe calculation of compound interest can involve complicated formulas. Our calculator provides a simple solution to address that difficulty. However, those who want a deeper understanding of how the calculations work can refer to the formulas below: Basic compound interest The basic formula for compound interest is as follows: At = A0(1 + r)n where: A0 : principal amount, or initial investment n : number of compounding periods, usually expressed in years In the following example, a depositor opens a $1,000 savings account. It offers a 6% APY compounded once a year for the next two years. Use the equation above to find the total due at maturity: At = $1,000 × (1 + 6%)2 = $1,123.60 For other compounding frequencies (such as monthly, weekly, or daily), prospective depositors should refer to the formula below. where: A0 : principal amount, or initial investment t : number of years Assume that the $1,000 in the savings account in the previous example includes a rate of 6% interest compounded daily. This amounts to a daily interest rate of: 6% ÷ 365 = 0.0164384% Using the formula above, depositors can apply that daily interest rate to calculate the following total account value after two years: At = $1,000 × (1 + 0.0164384%)(365 × 2) At = $1,000 × 1.12749 At = $1,127.49 Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to $1,127.49 at the end of two years. Continuous compound interest Continuously compounding interest represents the mathematical limit that compound interest can reach within a specified period. The continuous compound equation is represented by the equation below: At = A0ert where: A0 : principal amount, or initial investment e : mathematical constant e, ~2.718 For instance, we wanted to find the maximum amount of interest that we could earn on a $1,000 savings account in two years. Using the equation above: At = $1,000e(6% × 2) At = $1,000e0.12 At = $1,127.50 As shown by the examples, the shorter the compounding frequency, the higher the interest earned. However, above a specific compounding frequency, depositors only make marginal gains, particularly on smaller amounts of principal. Rule of 72 The Rule of 72 is a shortcut to determine how long it will take for a specific amount of money to double given a fixed return rate that compounds annually. One can use it for any investment as long as it involves a fixed rate with compound interest in a reasonable range. Simply divide the number 72 by the annual rate of return to determine how many years it will take to double. For example, $100 with a fixed rate of return of 8% will take approximately nine (72 / 8) years to grow to $200. Bear in mind that "8" denotes 8%, and users should avoid converting it to decimal form. Hence, one would use "8" and not "0.08" in the calculation. Also, remember that the Rule of 72 is not an accurate calculation. Investors should use it as a quick, rough estimation. History of Compound InterestAncient texts provide evidence that two of the earliest civilizations in human history, the Babylonians and Sumerians, first used compound interest about 4400 years ago. However, their application of compound interest differed significantly from the methods used widely today. In their application, 20% of the principal amount was accumulated until the interest equaled the principal, and they would then add it to the principal. Historically, rulers regarded simple interest as legal in most cases. However, certain societies did not grant the same legality to compound interest, which they labeled usury. For example, Roman law condemned compound interest, and both Christian and Islamic texts described it as a sin. Nevertheless, lenders have used compound interest since medieval times, and it gained wider use with the creation of compound interest tables in the 1600s. Another factor that popularized compound interest was Euler's Constant, or "e." Mathematicians define e as the mathematical limit that compound interest can reach. Jacob Bernoulli discovered e while studying compound interest in 1683. He understood that having more compounding periods within a specified finite period led to faster growth of the principal. It did not matter whether one measured the intervals in years, months, or any other unit of measurement. Each additional period generated higher returns for the lender. Bernoulli also discerned that this sequence eventually approached a limit, e, which describes the relationship between the plateau and the interest rate when compounding. Leonhard Euler later discovered that the constant equaled approximately 2.71828 and named it e. For this reason, the constant bears Euler's name. This compound interest calculator is a tool to help you estimate how much money you will earn on your deposit. In order to make smart financial decisions, you need to be able to foresee the final result. That's why it's worth knowing how to calculate compound interest. The most common real-life application of the compound interest formula is a regular savings calculation. Read on to find answers to the following questions:
You may also want to check our student loan calculator where you can make a projection on your expenses and study the effect of different student loan options on your budget.
In finance, interest rate is defined as the amount charged by a lender to a borrower for the use of an asset. So, for the borrower the interest rate is the cost of the debt, while for the lender it is the rate of return. Note that in the case where you make a deposit into a bank (e.g., put money in your savings account), you have, from a financial perspective, lent money to the bank. In such a case the interest rate reflects your profit. The interest rate is commonly expressed as a percentage of the principal amount (outstanding loan or value of deposit). Usually, it is presented on an annual basis, which is known as the annual percentage yield (APY) or effective annual rate (EAR).
Generally, compound interest is defined as interest that is earned not solely on the initial amount invested but also on any further interest. In other words, compound interest is the interest on both the initial principal and the interest which has been accumulated on this principle so far. Therefore, the fundamental characteristic of compound interest is that interest itself earns interest. This concept of adding a carrying charge makes a deposit or loan grow at a faster rate. You can use the compound interest equation to find the value of an investment after a specified period or estimate the rate you have earned when buying and selling some investments. It also allows you to answer some other questions, such as how long it will take to double your investment. We will answer these questions in the examples below.
You should know that simple interest is something different than the compound interest. It is calculated only on the initial sum of money. On the other hand, compound interest is the interest on the initial principal plus the interest which has been accumulated.
Most financial advisors will tell you that the compound frequency is the compounding periods in a year. But if you are not sure what compounding is, this definition will be meaningless to you… To understand this term you should know that compounding frequency is an answer to the question How often is the interest added to the principal each year? In other words, compounding frequency is the time period after which the interest will be calculated on top of the initial amount. For example:
Note that the greater the compounding frequency is, the greater the final balance. However, even when the frequency is unusually high, the final value can't rise above a particular limit. To understand the math behind this, check out our natural logarithm calculator. As the main focus of the calculator is the compounding mechanism, we designed a chart where you can follow the progress of the annual interest balances visually. If you choose a higher than yearly compounding frequency, the diagram will display the resulting extra or additional part of interest gained over yearly compounding by the higher frequency. Thus, in this way, you can easily observe the real power of compounding.
The compound interest formula is an equation that lets you estimate how much you will earn with your savings account. It's quite complex because it takes into consideration not only the annual interest rate and the number of years but also the number of times the interest is compounded per year. The formula for annual compound interest is as follows: FV = P (1+ r/m)^mt Where:
It is worth knowing that when the compounding period is one (m = 1) then the interest rate (r) is call the CAGR (compound annual growth rate).
Actually, you don't need to memorize the compound interest formula from the previous section to estimate the future value of your investment. In fact, you don't even need to know how to calculate compound interest! Thanks to our compound interest calculator you can do it in just a few seconds, whenever and wherever you want. (NB: Have you already tried the mobile version of our calculators?) With our smart calculator, all you need to calculate the future value of your investment is to fill the appropriate fields:
That's it! In a flash, our compound interest calculator makes all necessary computations for you and gives you the results. The two main results are:
In case you set the additional deposit field, we gave you the results for the compounded initial balance and compounded additional balance. Besides, we also show you their contribution to the total interest amount, namely, interest on the initial balance and interest on the additional deposit.
The following examples are there to try and help you answer these questions. We believe that after studying them, you won't have any trouble with the understanding and practical implementation of compound interest.
The first example is the simplest, in which we calculate the future value of an initial investment. Question You invest $10,000 for 10 years at the annual interest rate of 5%. The interest rate is compounded yearly. What will be the value of your investment after 10 years? Solution Firstly let’s determine what values are given, and what we need to find. We know that you are going to invest $10,000 - this is your initial balance P, and the number of years you are going to invest money is 10. Moreover, the interest rate r is equal to 5%, and the interest is compounded on a yearly basis, so the m in the compound interest formula is equal to 1. We want to calculate the amount of money you will receive from this investment, that is, we want to find the future value FV of your investment. To count it, we need to plug in the appropriate numbers into the compound interest formula: FV = 10,000 * (1 + 0.05/1) ^ (10*1) = 10,000 * 1.628895 = 16,288.95 Answer The value of your investment after 10 years will be $16,288.95. Your profit will be FV - P. It is $16,288.95 - $10,000.00 = $6,288.95. Note that when doing calculations you must be very careful with your rounding. You shouldn't do too much until the very end. Otherwise, your answer may be incorrect. The accuracy is dependent on the values you are computing. For standard calculations, six digits after the decimal point should be enough.
In the second example, we calculate the future value of an initial investment in which interest is compounded monthly. Question You invest $10,000 at the annual interest rate of 5%. The interest rate is compounded monthly. What will be the value of your investment after 10 years? Solution Like in the first example, we should determine the values first. The initial balance P is $10,000, the number of years you are going to invest money is 10, the interest rate r is equal to 5%, and the compounding frequency m is 12. We need to obtain the future value FV of the investment. Let's plug in the appropriate numbers in the compound interest formula: FV = 10,000 * (1 + 0.05/12) ^ (10*12) = 10,000 * 1.004167 ^ 120 = 10,000 * 1.647009 = 16,470.09 Answer The value of your investment after 10 years will be $16,470.09. Your profit will be FV - P. It is $16,470.09 - $10,000.00 = $6,470.09. Did you notice that this example is quite similar to the first one? Actually, the only difference is the compounding frequency. Note that, only thanks to more frequent compounding this time you will earn $181.14 more during the same period! ($6,470.09 - $6,288.95 = $181.14)
Now, let's try a different type of question that can be answered using the compound interest formula. This time, some basic algebra transformations will be required. In this example, we will consider a situation in which we know the initial balance, final balance, number of years and compounding frequency but we are asked to calculate the interest rate. This type of calculation may be applied in a situation where you want to determine the rate earned when buying and selling an asset (e.g., property) which you are using as an investment. Data and question Solution Let's try to plug this numbers in the basic compound interest formula: 3,000 = 2,000 * (1 + r/1) ^ (6*1) So: 3,000 = 2,000 * (1 + r) ^ (6) We can solve this equation using the following steps: 3,000 / 2,000= (1 + r) ^ (6) Raise both sides to the 1/6th power (3,000 / 2,000) ^ (1 / 6) = (1 + r) Subtract 1 from both sides (3,000 / 2,000) ^ (1 / 6) – 1 = r Finally solve for r r = 1.5 ^ 0.166667 – 1 = 1.069913 - 1 = 0.069913 = 6.9913% Answer In this example you earned $1,000 out of the initial investment of $2,000 within the six years, meaning that your annual rate was equal to 6.9913%. As you can see this time, the formula is not very simple and requires a lot of calculations. That's why it's worth testing our compound interest calculator, which solves the same equations in an instant, saving you time and effort.
Have you ever wondered how many years it will take for your investment to double its value? Besides its other capabilities, our calculator can help you to answer this question. To understand how it does it, let's take a look at the following example. Data and question You put $1,000 on your saving account. Assuming that the interest rate is equal to 4% and it is compounded yearly. Find the number of years after which the initial balance will double. Solution The given values are as follows: the initial balance P is $1,000 and final balance FV is 2 * $1,000 = $2,000, and the interest rate r is 4%. The frequency of the computing is 1. The time horizon of the investment t is unknown. Let's start with the basic compound interest equation: FV = P (1 + r/m)^mt Knowing that m = 1, r = 4%, and ‘FV = 2 * P we can write 2P = P (1 + 0.04) ^ t Which could be written as 2P = P (1.04) ^ t Divide both sides by P (P mustn't be 0!) 2 = 1.04 ^ t To solve for t, you need take the natural log (ln), of both sides: ln(2) = t * ln(1.04) So t = ln(2) / ln(1.04) = 0.693147 / 0.039221 = 17.67 Answer In our example it takes 18 years (18 is the nearest integer that is higher than 17.67) to double the initial investment. Have you noticed that in the above solution we didn't even need to know the initial and final balances of the investment? It is thanks to the simplification we made in the third step (Divide both sides by P). However, when using our compound interest rate calculator, you will need to provide this information in the appropriate fields. Don't worry if you just want to find the time in which the given interest rate would double your investment, just type in any numbers (for example 1 and 2). It is also worth knowing that exactly the same calculations may be used to compute when the investment would triple (or multiply by any number in fact). All you need to do is just use a different multiple of P in the second step of the above example. You can also do it with our calculator.
Compound interest tables were used everyday, before the era of calculators, personal computers, spreadsheets, and unbelievable solutions provided by Omni Calculator 😂. The tables were designed to make the financial calculations simpler and faster (yes, really…). They are included in many older financial textbooks as an appendix. Below, you can see what a compound interest table looks like.  Using the data provided in the compound interest table you can calculate the final balance of your investment. All you need to know is that the column compound amount factor shows the value of the factor (1 + r)^t for the respective interest rate (first row) and t (first column). So to calculate the final balance of the investment you need to multiply the initial balance by the appropriate value from the table. Note that the values from the column Present worth factor are used to compute the present value of the investment when you know its future value. Obviously, this is only a basic example of a compound interest table. In fact, they are usually much, much larger, as they contain more periods t various interest rates r and different compounding frequencies m... You had to flip through dozens of pages to find the appropriate value of compound amount factor or present worth factor. With your new knowledge of how the world of financial calculations looked before Omni Calculator, do you enjoy our tool? Why not share it with your friends? Let them know about Omni! If you want to be financially smart, you can also try our other finance calculators.
Now that you know how to calculate compound interest, it's high time you found other applications to help you make the greatest profit from your investments: To compare bank offers which have different compounding periods, we need to calculate the Annual Percentage Yield, also called Effective Annual Rate (EAR). This value tells us how much profit we will earn within a year. The most comfortable way to figure it out is using the APY calculator, which estimates the EAR from the interest rate and compounding frequency. If you want to find out how long it would take for something to increase by n%, you can use our rule of 72 calculator. This tool enables you to check how much time you need to double your investment even quicker than the compound interest rate calculator. You may also be interested in the credit card payoff calculator, which allows you to estimate how long it will take until you are completely debt-free. Another interesting calculator is our cap rate calculator which determines the rate of return on your real estate property purchase. We also suggest you try the lease calculator which helps you determine the monthly and total payments for a lease. If you're looking to finance the purchase of a new recreational vehicle (RV), our RV loan calculator makes it simple to work out what the best deal will be for you. The depreciation calculator enables you to use three different methods to estimate how fast the value of your asset decreases over time. And finally, why not to try our dream come true calculator. |
Find the compound interest when principal 2000 rate 20% per annum and time = 2 years 3 months
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